Communications in Computational and Applied Mathematics, Vol. 2 No. 1 (2020) p. 1-6 CCAM Communications in Computational and Applied Mathematics Journal homepage : www.fazpublishing.com/ccam e-ISSN : 2682-7468 Systematic Satisfiability Programming in Hopfield Neural Network- A Hybrid Expert System for Medical Screening Mohd Shareduwan Mohd Kasihmuddin1, Mohd. Asyraf Mansor2,*, Siti Zulaikha Mohd Jamaludin3, Saratha Sathasivam4 1,3,4School of Mathematical Sciences, Universiti Sains Malaysia, Minden, Pulau Pinang, Malaysia 2School of Distance Education, Universiti Sains Malaysia, Minden, Pulau Pinang, Malaysia *Corresponding Author Received 26 January 2020; Abstract: Accurate and efficient medical diagnosis system is crucial to ensure patient with recorded Accepted 12 February 2020; system can be screened appropriately. Medical diagnosis is often challenging due to the lack of Available online 31 March patient’s information and it is always prone to inaccurate diagnosis. Medical practitioner or 2020 specialist is facing difficulties in screening the disease accurately because unnecessary attributes will lead to high operational cost. Despite of acting as a screening mechanism, expert system is required to find the relationship between the attributes that lead to a specific medical outcome. Data mining via logic mining is a new method to extract logical rule that explains the relationship of the medical attributes of a patient. In this paper, a new logic mining method namely, 2 Satisfiability based Reverse Analysis method (2SATRA) will be proposed to extract the logical rule from medical datasets. 2SATRA will capitalize the 2 Satisfiability (2SAT) as a logical rule and Hopfield Neural Network (HNN) as a learning system. The extracted logical rule from the medical dataset will be used to diagnose the final condition of the patient. The proposed 2SATRA will utilize four prominent datasets that focuses on well-known medical disease such as Hepatitis, Diabetes and Cancer. This paper utilizes Diabetic Retinopathy Debrecen, Pima Indians Diabetes, Hepatitis and Mammographic Mass datasets that were obtained from established repository. The efficiency of 2SATRA is evaluated in terms of performance error and computation time. The results obtained for all medical data sets of 2SATRA achieved acceptable accuracy. Keywords: Hopfield Neural Network; Logic Mining; Medical Screening 1. Introduction because the main objective of ANN is to replicate the human Medical screening is a vital part of a healthy lifestyle. intelligence with astonishing computation capability. The Regular health check-up will help us detect early potential growing attention towards the ANN as a model for AI is due health problem. Most of the medical practitioner utilized to the capability of ANN in representing the model in terms of preventive health screening to analyze the condition of our mathematical equations. One of the most appreciated simple body. Patients will supply them with data (from the health ANN is Hopfield Neural Network (HNN). Popularized by screening) and the medical practitioner will classify the Hopfield, HNN [1] has been utilized to solve various both condition of the patient. Medical practitioner experienced high constrained and unconstrained optimization problem. HNN frequent of misdiagnosed due to several factors such as consists of interconnected neurons that updates missing data, unnecessary attributes and error in medical asynchronously as the dynamic of the network changes. The instruments. In that regard, the intelligent system is required quality of the solution for HNN is represented in terms of to learn the past data and utilize it to predict and classify the energy function. The main focus of the HNN model is to find current patient. Hence, a more accurate and efficient system is the solution that corresponds to the minimum Lyapunov very crucial in the field of medicine. Energy function. To serve as a useful method, the training of Artificial intelligence (AI) is a prominent field of science HNN must be conducted in an efficient and effective manner. that specializes in data modelling. The subfield of AI, Considering the network architecture, input of the neurons Artificial Neural Network (ANN) gained its popularity will be excited to generate the synaptic weight of the system [2, 3]. Fault tolerance and content addressable memory *Corresponding author: [email protected] 2020 FAZ Publishing. All right reserved. Mohd Kasihmuddin et. al., Communications in Computational and Applied Mathematics, Vol. 2 No. 1 (2020) p. 1-6 properties contribute to the popularity of HNN in processing simulation results indicate the proposed logic mining is able and constructing the pattern of the data. In another to classify diabetic patients with high accuracy. development, the beneficial feature of HNN is implemented in The work is organized as follows. Section 2 and 3 present the field of health sciences. Chang and Chung [4] proposed the overview of 2-SAT representation and 2SAT utilization in HNN in medical image segmentation. In this paper, the image HNN respectively. In Section 4, the formation of 2SATRA segmentation produced by HNN is more continuous and used to undertake the medical data sets is presented. The smoother compared to other methods. Hsu [5] proposed fuzzy attained results and limitations encountered in this experiment HNN in clustering electroencephalogram data. The proposed are presented in Section 5. Conclusions and future work method is used to classify left and right medical imagery data directions are given in Section 6. with acceptable accuracy compared to other popular classifiers. Sammouda [6] improvised the usage of HNN in 2. 2 Satisfiability Representation performing pathological liver colour images. The proposed 2 Satisfiability or (2SAT) is variant of generalized HNN is evaluated based on 20 real pathological liver data that Satisfiability representation kSAT that consists of exactly 2 consist of various colour images and was reported to be literals per clause. 2SAT formulation can be expressed in effective in data segmentation. These applications raised an terms of 2 Conjunctive Normal Form (2CNF). 2SAT can be important question: what is the most effective method to identified based on the following criteria [10]: extract important information from the medical dataset but at 1. A set of l variables, x, x ,......, x . the same time the extracted information is readable by the 12 l user? 2. A set of literals and each literal can be a positive or Logic programming in HNN is initially proposed by Wan negative (negation). Abdullah [7] by incorporating logical rule in Hopfield Neural 3. A set of m distinct clauses: Ci here im1,2,3,..., . Network. The proposed network obtains synaptic weight by C is connected to C by conjunction ( ). The 2 comparing the cost function with the final energy function. i i1 The quest of creating optimal HNN is continued by literals inside each Ci is connected by disjunction ( Sathasivam [8] where the proposed HNN is incorporated with ). Horn clause. The usage of Horn clause is considered effective In general, each of the variables consists of the because the proposed logical rule is always satisfiable. In information which contributes the nature of the combinatorial order to comply with real life problem, Sathasivam and problem. The state for each 2SAT variable in each C is Abdullah [9] proposed Reverse Analysis method to extract i valuable logical rule from the real-life dataset. One of the given as -1 (FALSE) and 1 (TRUE). 2SAT formulation can be limitations of the proposed Reverse Analysis is the flexibility defined explicitly as follows: of the logical rule to extract the optimal logical rule. Despite having high value of global minima ratio, the induced logical m PC2SAT i (1) rule is not able to effectively generalize the real-life dataset. i1 The scope of the real-life dataset used in the proposed Reverse Analysis is also limited to small data points. In another where each clause C is given as follows: development, Kasihmuddin et al. [10, 11] proposed a new i systematic logical rule namely 2 Satisfiability (2SAT) in HNN. The proposed logical rule has been optimized by using n Ci x i, y i (2) Metaheuristics Algorithm [11, 12] and the proposed method i1 managed to achieve global minimum solution. The usage of 2SAT in HNN has been extended to several applications such as Pattern Satisfiability [13] and Very Large-Scale Integration One of the example of P2SAT instance based on Equations (1) (VLSI) [14]. The recent works demonstrated the practical and (2) is: usage of 2SAT in Mutation HNN [10] and Radial Basis Function Neural Network [15]. P2SAT x 1 x 2 x 3 x 4 (3) Unfortunately, the usage of 2SAT in Reverse Analysis method is still poorly understood. In this case, there is no recent innovation to extract important logical rule in the One possible variable assignation that would satisfy medical datasets. Hence, the contributions of this paper are: Equation (3) is x1, x 2 , x 3 , x 4 , x 5 1, 1, 1,1 . In this case, (1) This paper explores the representation of the dataset by both clauses C1 and C2 are satisfied CC121, 1 that lead using 2SAT logical rule. (2) A novel logic mining method via 2 Satisfiability Reverse Analysis method is proposed by to P2SAT 1 . On the other hand, Equation (3) shows logical implementing 2SAT as a systematic logical rule in HNN. The inconsistencies P2SAT 1 if one of the clauses does not functionality of the proposed methods is divided into 2 parts. satisfied C 1. Note that, the state of variable in each C The first part discusses the implementation of 2SAT in HNN. i i The later part will explain the implementation of HNN in 2 exhibits useful logical informations that contribute the Satisfiability Based Reverse Analysis method. (3) Logic outcome of the P2SAT . In this case, we choose k 2 Mining will be used to extract the logical relationship that because we only consider two-dimensional relationship explains the behaviour of the medical datasets.